## Physics Questions People Ask Fermilab

**Proof of Kepler's law?**

**You Wrote:**

I have this homework question, my physics teacher said that you can prove Kepler's second law with one quantity of measurement. He hinted us with Mass and that is all he gave....Can you help me on what measurement it is that I need to prove Kepler's second law.

thanx a million

mark

Mark,

Greetings, Kepler's second law is that a planet travelling in an elliptical orbit around the sun sweeps out equal areas in equal times. This is basically a statement of conservation of angular momentum. Area A is proportional to R**2 times theta, where theta is the angular displacement of the planet in a given time, and R is the distance from the planet to the sun. Since R**2 times Theta is also proportional to the angular momentum, constant angular momentum implies constant A. The result is that Theta is inversely proportional to R**2. If I wanted to confirm this from the ground, I'd look at the apparent area of the sun, which is also inversely proportional to R**2. Then I'd look at the motion of the sun in the sky (relative to the stars, of course) to infer the angular velocity of the earth. If Kepler's 2nd law is true then the angular velocity should be proportional to the apparent area of the sun.

Hope that helps,

Michael B. Crisler

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